Chaotic dynamics, basin structure and global dynamical analysis of a six-dimensional series memcapacitor system

This research presents a nonlinear dynamical analysis of a six-dimensional series-connected memcapacitor system, focusing on its equilibrium structure, dissipativity, bounded dynamics, invariant properties, and chaotic behaviour. The coupled nonlinear memory interactions provide a framework for complex electrical dynamics. Analytical examination identifies a non-isolated equilibrium manifold, while the negative phase-space divergence establishes volume contraction and supports formation of a bounded dissipative attractor. A numerical protocol was employed using fourth-order Runge–Kutta integration with step size 0.001, total integration time 10,000, and removal of the first 5,000 time units as transient dynamics. The Lyapunov spectrum was evaluated using periodic QR re-orthonormalization. At the investigated parameter set, the validated spectrum is λ₁ = 8.244 × 10⁻ 2 , λ₂ = 9.897 × 10⁻ 5 , λ₃ = 2.577 × 10⁻⁸, λ₄ = −1.250 × 10⁻ 4 , λ₅ = −3.469 × 10⁻ 4 , and λ₆ = −6.075 × 10⁻ 1 . Only one exponent exceeds the positive threshold, establishing chaotic dynamics. The sum of the Lyapunov exponents agrees with the time-averaged divergence, with an error of 5.878 × 10⁻⁹, while the conserved v₁−v₂ relation is satisfied to numerical precision. Time series, phase-space projections, three-dimensional trajectories, Poincaré section, power spectral density, and Lyapunov convergence analyses provide complementary evidence of deterministic aperiodic dynamics. These results establish a theoretically grounded framework for understanding chaos generated by coupled memcapacitive interactions and provide a basis for investigations of parameter-dependent transitions, attractor organization, synchronization, and control.